Problem: $A$ $B$ $C$ If: $ AB = 2x + 3$, $ BC = 3x + 9$, and $ AC = 47$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {2x + 3} + {3x + 9} = {47}$ Combine like terms: $ 5x + 12 = {47}$ Subtract $12$ from both sides: $ 5x = 35$ Divide both sides by $5$ to find $x$ $ x = 7$ Substitute $7$ for $x$ in the expression that was given for $BC$ $ BC = 3({7}) + 9$ Simplify: $ {BC = 21 + 9}$ Simplify to find ${BC}$ : $ {BC = 30}$